What is the solution for 9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=3 ?

The solution for 9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=3 is y=2e^{(2t)/3}+(5e^{(2t)/3}t)/(3)

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9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=3

9 y^{^{''}} - 12 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 3

y = 2 e^{\frac{2 t}{3}} + \frac{5 e ^{\frac{2 t}{3}} t}{3}

Solution steps

9 y^{''} (t) - 12 y^{'} (t) + 4 y = 0

Solve linear ODE:

y = 2 e^{\frac{2 t}{3}} + \frac{5 e ^{\frac{2 t}{3}} t}{3}

y = 2 e^{\frac{2 t}{3}} + \frac{5 e ^{\frac{2 t}{3}} t}{3}

y^{^{''}} - 8 y^{^{'}} - 33 y = 0, y (0) = 0, y^{^{'}} (0) = - 7

y^{^{''}} + y = 0

3 y^{^{'''}} + 10 y^{^{''}} + 15 y^{^{'}} + 4 y = 0

y^{^{''}} + 0.25 y^{^{'}} + y = 0, y (0) = 2, y^{^{'}} (0) = 0

y^{^{''''}} = 16 y

What is the solution for 9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=3 ?
The solution for 9y^{''}-12y^'+4y=0,y(0)=2,y^'(0)=3 is y=2e^{(2t)/3}+(5e^{(2t)/3}t)/(3)